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Trägheitsmoment einer quadratischen Pyramide

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Exercise

https://texercises.com/exercise/tragheitsmoment-einer-quadratischen-pyramide/

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Exercise:
Berechne das Trägheitsmoment einer quadratischen Pyramide mit der Masse m und der Seitenlänge a.

Solution:
I op r^ rm d m varrhoop r^ rm d V varrhoop r^ rm d z rm d y rm d x varrhoop x^+y^ rm d z rm d y rm d x varrhoop_^h rm d z op_-fracazh^fracazh rm d y op_-fracazh^fracazh rm d x x^ + y^ varrhoop_^h rm d z op_-fracazh^fracazh rm d y leftfrac x^ + y^xright_-fracazh^fracazh varrhoop_^h rm d z op_-fracazh^fracazh rm d y leftfrac frac a^z^h^ + y^ fracazh - frac frac -a^z^h^ - y^ frac -azh right varrhoop_^h rm d z op_-fracazh^fracazh rm d y left frac a^z^h^ + y^ fracazh right varrhoop_^h rm d z left frac a^z^yh^ + fracazy^h right_-fracazh^fracazh varrhoop_^h rm d z leftfrac a^z^h^ + fraca^z^h^ right x varrhoop_^h rm d z left frac a^z^h^ right varrho left frac a^z^h^ right_^h varrho left frac a^h right varrho left frac a^ a^ h right varrho underbraceleft frac a^a^h right_fraca^h V varrho V left frac a^ right fracma^

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Contained in these collections:

Trägheitsmomente by pw

4 | 4
Alternativen zum KKW Gösgen by pw

3 | 3

Attributes & Decorations

Tags	körper, pam, pyramide, quadratische, starrer, trägheitsmoment
Content image
Difficulty	(4, default)
Points	4 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	pw
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